Question

A 120-foot-long rope is cut into 3 pieces. The
first piece of rope is twice as long as the second
piece of rope. The third piece of rope is three
times as long as the second piece of rope.
What is the length of the longest piece of rope?

Answer 1

Let the three pieces of the rope be x,y, and z respectively.

1) x=2y
2) z=3y
(Note: We deduce from these 2 equations that the longest part we want to find is z)

3) x+y+z=120

Substitute 1) and 2) in 3)
Hence we get: 2y+y+3y=120;
6y=120 ==> y=20 ft

Therefore, z=3y=60 ft